Supposedly... does it actually work for you? It doesn't work for me so far except with iMessage (which worked in iOS 6 too).
Edit: As noted below Facebook does this too, I'm not sure if it's the iOS 7 sync of it's Facebook's own infrastructure that updates the badge in the background.
Yeah, the only thing I have seen it work with is iMessage & Facebook.
I have a couple of sports apps sending the same notifications to both iPad & iPhone and have to clear both devices separately.
I've been wondering the same thing. Syncing has always worked for iMessage alerts, but I haven't gotten it to work for anything else. It's my only issue with iOS.